A wallet is the user-friendly interface you interact with to manage your account (s)
An account is a pair of public and private keys that "hold" your funds. They do not actually hold your funds since your funds are stored on the blockchain.
You can imagine that a private and public key pair as the username (public) and password (private) you use on Twitter. For additional security you can use a password to encrypt your private key which would result in a username (public) and password (private) along with a password for that password (private and more secure).
Examples of a wallet are imToken, MyEtherWallet.com and a Ledger hardware wallet.